Hello 2+2,

UTG w/ AK. $86 in front of me (smallest stack). 1/2 game

I limp UTG and get 5 calls before button makes it $12 to go. I raise to $36 and get 2 callers (including button). Pot is now $120. Flop is QJ3. I'm first to act and push my remaining $50 into the pot. I figure there's a great possibility even if the flop connected with the villians, I have about 40 percent equity at this point.

MP calls and button raises to $150, thus pushing out MP. So I basically am 220:50 or 4.4:1 on my money.

Turns out button has AQ and I'm drawing to 7 outs. So I have about 30 percent equity or 2.3:1. So I'm winning $220 while losing $115 for a +EV of $105 per hand.

Button, on the other hand, is also $220:50 on his money and will win 2.3:1, thus he is losing $50 while winning $506, for a +EV of $456 per hand. For some reason, I feel my math is off.

1) Is my math corrrect here? Am I missing something?
2)I'm happy I am +EV here but unhappy at the amazing +EV of button. Do you take the EV you offer opponents into consideration or are you happy getting in any spots that offer you +EV?
3)Could I have played this hand any better? Maybe offer crappier odds preflop. The button was $90:24 or 3.7:1, which is better than his 2.3:1 odds AQ vs AK. I feel like I should have pushed preflop, or check/fold turn? Maybe my only move there is push pre. What do you think?

Any thoughts and replies are greatly appreciated. Thank you.

If I push my pre, and MP folds, button is $108:74 on his money, which is a lot better. So with his AQ being 1:2.3 vs my AK, he is winning $108 while losing $170. -EV of $62 per hand.

While I would be about $180:86 on my money, which means I'm winnng +- $420 and losing $86 for +EV $334. So I think best play is pushing pre. Thoughts?

I'm pretty bad at math, so hopefully if I'm wrong someone would correct me.

Your EV on the flop once all the money has gone in is 270 (the total pot) * .3 (your equity) = $81. That $81 is the amount you expect to win in the long run. If we take that $81 and minus the amount that you had to put in on the flop, $50, we arrive at $31. This is the amount of money in the long run that you can expect to win through the sequence of events on the flop and how it ended up (this is just in absolute terms and excluding ranges, etc).

The mathematical equation for this would be either;

(270)(.3) - 50 = 31 OR
(220)(.3) + (-50)(.7)

In the first case we take your equity share of the pot and minus the amount you had to call. In the second case we take the amount of the pot, excluding your call, and multiply this by your chance of winning. Then we add this to the amount you had to call and multiply it by the chance of you losing.

As to your second question, I think that two people can both be +EV in an AI situation due to dead money in the pot and it's not necessarily a bad thing.

You definitely should have shoved pre though. There's $24 in the pot, just shove and be happy if you take it down PF. You also have amazing equity vs the average calling range so don't worry about it. If you make it $36 and even get called in 1 spot you have a bit more than 1/2PSB on the flop and have terrible FE.

Exactly right. It's not unusual for two people both to be in a +EV situation.

This case is typical.

The key point is that: Just because you're making a +EV call doesn't mean your making money playing the hand. A lot of the money you're winning is money that was in your own stack when the hand started, that is now dead money.

Obviously the OP is losing money every time he has AK versus AQ and runs into a QJ3 flop.

If there's 270 in the pot and you have 28% equity, then 270 * .28 is 75.60. Since the OP started the hand with 86 dollars. He's losing 10.40 every time this happens.

The optimal play in this hand, after you limp, is to shove pre. It's not even close.

Like, the sole reason you would limp here is for the opportunity to shove in a +++EV situation. If you can't do this, you must raise it up yourself.

Think of it like this...there was over $20 in the pot already when it got back to you. That was 1/4 of your chip stack. A good % of the time you are going to pick that up for free. And, if you do get called, AK is in ok shape versus their ranges given the stupid limps.

This was a serious mistake and a sign that you need to work on your short stack poker if you're going to be playing with 40 bb in front of you.

Flop is w/e, you're never folding here given your equity unless the action is insane so you might as well stick it in yourself and hope they all fold.

Keep in mind you're playing against a range of hands, and the focus of your analysis should really be on how you're doing relative to their range.

Also his EV isn't really -62. What matters is the EV for his marginal action. What he has bet already is a sunk cost. He has two choices if you shove pre:

- Call for $74 more
- Fold and lose the $12 he's already bet plus the chance to win the other ~$91 that's in the pot (5 limps of $2 plus your $86 stack minus a $5 assumption about rake.)

His EV is no where near as low as -62. It's still negative, but not nearly that bad. And, keep in mind that he's playing against your range of hands, not AK. His play is still bad against that range, IMO, but, hey, that's how we make money at this game!

Just to illustrate this point with an EV calculation given the info The Rumor provided here.

The EV for villains call against a range of 88+ / AK: He has 34% equity PF

(.34)(103) + (.66)(-74) = -13.8. So button is losing $-13.8 every time he calls your Preflop shove

The EV for villain if he knows you have AK: He has 25% equity PF

(.25)(103) + (.75)(-74) = -29.75

So it's definitely a negative EV call for him, but not as much as you we estimating Ralphizzle. But given the players at this limit he's going to call here pretty much always so you have a very profitable situation if you shove pre here.

Why are you sitting at a 1/2 game with $86 in front of you?? You need to buy-in full and top off as you play. When you go to the cage, buy $300 in chips. Get $200 in red and $100 in green. Stick the $100 in green in your pocket, and top off anytime that you drop below $175.

There is no point in playing with less than a full buy-in on the table. It's a huge leak to sit at the table with ~40 BB's.

GL

Shove PF .. You didn't even raise the pot and once someone calls you are committed to the pot regardless. Just get it in now.

Top off, yes ...

AP .. You are better off trying to get this to check through than shoving and giving zero-additional-risk odds to the callers on this Flop. Yes, I know I said you were pot committed, but I didn't say you had to voluntarily put it in there! Is anyone going to fold here if you show AA to them and they've connect somehow? No. ... GL